59.1.127 problem 129

Internal problem ID [9299]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 129
Date solved : Monday, January 27, 2025 at 06:01:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.369 (sec). Leaf size: 32

dsolve(9*x^2*diff(y(x),x$2)+3*x*(5+3*x-2*x^2)*diff(y(x),x)+(1+12*x-14*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {x \left (x -3\right )}{3}} \left (\left (\int \frac {{\mathrm e}^{-\frac {x \left (x -3\right )}{3}}}{x}d x \right ) c_{2} +c_{1} \right )}{x^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.476 (sec). Leaf size: 52

DSolve[9*x^2*D[y[x],{x,2}]+3*x*(5+3*x-2*x^2)*D[y[x],x]+(1+12*x-14*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\frac {1}{3} (x-3) x} \left (c_2 \int _1^x\frac {e^{K[1]-\frac {K[1]^2}{3}}}{K[1]}dK[1]+c_1\right )}{\sqrt [3]{x}} \]